Group #14560084 — subgroups

Subgroups — C₁₉×#2227 #14560084

Order 2432.

130 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#500	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#366	C₂	1	2	yes	maximal
4	C₁₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#358	C₂	1	2	yes	maximal
6	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×C₄⋊Q₈	—	2	1	no	—
8	C₄×Q₈×C₁₉	—	2	1	no	—
9	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
10	C₁₉×#107	—	2	1	no	—
11	C₁₉×#107	C₂²	1	2	yes	—
12	C₁₉×#107	C₂²	1	1	yes	characteristic
13	C₁₉×#103	—	2	1	no	—
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₁₉	—	2	1	no	—
16	C₂×Q₈×C₁₉	—	4	1	no	—
17	Q₁₆×C₁₉	—	2	1	no	—
18	Q₁₆×C₁₉	Q₈	1	2	yes	complemented
19	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₁₉	—	2	1	no	—
22	C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₄⋊C₄×C₁₉	—	4	1	no	—
24	C₄⋊C₄×C₁₉	—	4	1	no	—
25	C₄²×C₁₉	—	4	1	no	—
26	C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₁₆×C₁₉	—	2	2	no	—
28	Q₈×C₁₉	—	2	2	no	—
29	Q₈×C₁₉	—	4	1	no	—
30	Q₈×C₁₉	—	8	2	no	—
31	C₂×C₄×C₁₉	—	4	1	no	—
32	C₂×C₄×C₁₉	—	4	1	no	—
33	C₂×C₄×C₁₉	—	4	2	no	—
34	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
35	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₈×C₁₉	—	2	1	no	—
38	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
39	C₈×C₁₉	#41	1	1	yes	characteristic
40	#2227	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
42	C₄×C₁₉	—	2	1	no	—
43	C₄×C₁₉	—	4	2	no	—
44	C₄×C₁₉	—	8	1	no	—
45	C₄×C₁₉	—	8	2	no	—
46	C₄×C₁₉	Q₃₂	1	2	yes	—
47	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
48	C₄×C₁₉	#137	1	1	yes	characteristic
49	#500	C₂×C₁₉	1	1	yes	characteristic
50	C₄×Q₁₆	C₂×C₁₉	1	1	yes	characteristic
51	#366	C₂×C₁₉	1	2	yes	—
52	C₄⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic
53	#358	C₂×C₁₉	1	2	yes	—
54	C₂×C₁₉	#474	1	1	yes	characteristic
55	C₂×C₁₉	C₂×Q₃₂	1	1	yes	characteristic
56	C₂×C₁₉	#509	1	1	yes	characteristic
57	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
58	C₄⋊Q₈	—	2	1	no	—
59	C₄×Q₈	—	2	1	no	—
60	C₂×C₁₆	C₂²×C₁₉	1	2	yes	—
61	#107	—	2	1	no	—
62	#107	C₂²×C₁₉	1	2	yes	—
63	#107	C₂²×C₁₉	1	1	yes	characteristic
64	#103	—	2	1	no	—
65	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
66	C₁₉	#2227	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×Q₈	—	2	1	no	—
68	C₂×Q₈	—	4	1	no	—
69	Q₁₆	—	2	1	no	—
70	Q₁₆	Q₈×C₁₉	1	2	yes	complemented
71	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
72	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
73	C₄⋊C₄	—	2	1	no	—
74	C₄⋊C₄	—	2	2	no	—
75	C₄⋊C₄	—	4	1	no	—
76	C₄⋊C₄	—	4	1	no	—
77	C₄²	—	4	1	no	—
78	C₄²	D₄×C₁₉	1	1	yes	characteristic
79	C₁₆	—	2	2	no	—
80	Q₈	—	2	2	no	—
81	Q₈	—	4	1	no	—
82	Q₈	—	8	2	no	—
83	C₂×C₄	—	4	1	no	—
84	C₂×C₄	—	4	1	no	—
85	C₂×C₄	—	4	2	no	—
86	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
87	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
88	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
91	C₈	#41×C₁₉	1	1	yes	characteristic
92	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	4	2	no	—
95	C₄	—	8	2	no	—
96	C₄	—	8	1	no	—
97	C₄	C₁₉×Q₃₂	1	2	yes	—
98	C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
99	C₄	C₁₉×#137	1	1	yes	characteristic
100	C₂	C₁₉×#474	1	1	yes	characteristic
101	C₂	C₂×C₁₉×Q₃₂	1	1	yes	characteristic
102	C₂	C₁₉×#509	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#500

C₂

yes

maximal, characteristic

C₄×Q₁₆×C₁₉

C₂

yes

maximal, characteristic

C₁₉×#366

C₂

yes

maximal

C₁₉×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₁₉×#358

C₂

yes

maximal

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₄×Q₈×C₁₉

—

C₂×C₁₆×C₁₉

C₂²

yes

—

C₁₉×#107

—

C₁₉×#107

C₂²

yes

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#103

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

Q₈

yes

complemented

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₁₆×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₂×Q₈

yes

C₈×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

Q₃₂

yes

—

C₄×C₁₉

C₂²⋊Q₈

yes

C₄×C₁₉

yes

C₂×C₁₉

yes

characteristic

C₄×Q₁₆

C₂×C₁₉

yes

characteristic

#366

C₂×C₁₉

yes

—

C₄⋊C₁₆

C₂×C₁₉

yes

characteristic

#358

C₂×C₁₉

yes

—

C₂×C₁₉

#474

yes

characteristic

C₂×C₁₉

C₂×Q₃₂

yes

characteristic

C₂×C₁₉

#509

yes

characteristic

C₂×Q₁₆

C₂²×C₁₉

yes

characteristic

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₁₆

C₂²×C₁₉

yes

—

#107

—

#107

C₂²×C₁₉

yes

—

#107

C₂²×C₁₉

yes

characteristic

#103

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2227

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

Q₈×C₁₉

yes

complemented

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

D₄×C₁₉

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₈×C₁₉

yes

characteristic

C₂×C₄

D₈×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₈

—

C₈

C₂×Q₈×C₁₉

yes

characteristic

C₈

#41×C₁₉

yes

characteristic

C₂²

C₂×D₈×C₁₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

C₁₉×Q₃₂

yes

—

C₄

C₁₉×C₂²⋊Q₈

yes

characteristic

C₄

C₁₉×#137

yes

characteristic

100

C₂

C₁₉×#474

yes

characteristic

101

C₂

C₂×C₁₉×Q₃₂

yes

characteristic

102

C₂

C₁₉×#509

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₁₉

C₂×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
18. Q₁₆×C₁₉	Q₈	semidirect
40. #2227	C₁₉	direct (N × H)
66. C₁₉	#2227	direct (N × H)
70. Q₁₆	Q₈×C₁₉	semidirect

H ≅ G/N

type

18. Q₁₆×C₁₉

Q₈

semidirect

40. #2227

C₁₉

direct (N × H)

66. C₁₉

#2227

direct (N × H)

70. Q₁₆

Q₈×C₁₉

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#500	2
C₄×Q₁₆×C₁₉	2
C₁₉×#366	2
C₁₉×C₄⋊C₁₆	2
C₁₉×#358	2
#2227	19

subgroup

index

C₁₉×#500

C₄×Q₁₆×C₁₉

C₁₉×#366

C₁₉×C₄⋊C₁₆

C₁₉×#358

#2227

Subgroups — C₁₉×#2227 #14560084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2227 #14560084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2227 #14560084